![4 [20 Points] Derive the Huffman tree for the symbols with probabilities given below. Show the codewords for the symbols and](http://img.homeworklib.com/questions/f0931940-2167-11ec-9394-df2059c9f359.png?x-oss-process=image/resize,w_560)
Homework Answers
Answer:---------
The Huffman tree is the binary tree with minimum external path weight, i.e., the one with the minimum sum of weighted path lengths for the given set of leaves. So the goal is to build a tree with the minimum external path weight.
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4 [20 Points] Derive the Huffman tree for the symbols with probabilities given below. Show the...
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities...
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
4. Consider the given seven symbols with probabilities as {A, B, C, D, E, F, G}...
4. Consider the given seven symbols with probabilities as {A, B, C, D, E, F, G} = {0.25, 0.20, 0.18, 0.15, 0.12, 0.06, 0.04}. Use Huffman coding to determine coding bits, entropy and average bits per symbol.
(4) Given the following frequencies of letters appearing in a file, use Huffman Coding to determine...
(4) Given the following frequencies of letters appearing in a file, use Huffman Coding to determine the average number of bits used to encode a symbol, the binary code used to represent each bit, and the resulting binary tree. (20 pts.) A: 0.08, B: 0.10, C: 0.12, D: 0.15, E: 0.20, F: 0.35
3. Apply the Huffman algorithm according to the frequency chart shown below. (10 points) a. Show...
3. Apply the Huffman algorithm according to the frequency chart shown below. (10 points) a. Show your work for combining the characters and frequencies. b. Assemble and show the finished tree. c. State the encoding for each character. d. Show your calculation and state the compression ratio. e. Using your Huffman tree from this question, encode the string ABACABAD. f. Using your Huffman tree from this question, decode the bit-string 100010111001010. symbol A B C D frequency 0.4 0.1 0.2...
Find the optimal binary symbol code using the Huffman coding algorithm. Draw the Huffman tree (show...
Find the optimal binary symbol code using the Huffman coding algorithm. Draw the Huffman tree (show intermediate steps) and list the final prefix code for each letter. letter : { a b c d e f g } frequency: {.01, .24, .05, .20, .47, .01, .02}
9. (4) Select the best choice as Huffman code for the following symbols and their probabilities:...
9. (4) Select the best choice as Huffman code for the following symbols and their probabilities: A-0.10 C-0.17 E-0.21 B-0.21 D-0.06 F-0.25 (a) A: O, B: 10, C: 110, D: 1110, E: 11110, F: 11111 (b) A: 0,B: 10, C: 11111, D: 1110, E: 11110, F: 110 (c) A: 11110, B: 10, C: 1110, D: 11111, E: 110, F: 0 (d) A: 11111, B: 11110, C: 1110, D: 110, E: 10, F: 0 (e) A: 0,B: 01, C: 0001, D:...
Design the optimal (Huffman) code for the alphabet {a, b, c, d, e, f, g, h,...
Design the optimal (Huffman) code for the alphabet {a, b, c,
d, e, f, g, h, i, j, k, l}, where frequencies are given in the
table below:
Draw the appropriate decoding tree.
a 0.25 g 0.02 b 0.01 h 0.12 c 0.09 i 0.15 d 0.02 j 0.04 e 0.24 k 0.01 f 0.04 l 0.01
You will construct a Huffman tree based on the given frequencies of 26 English alphabets in...
You will construct a Huffman tree based on the given frequencies of 26 English alphabets in upper case plus the space character. An internal tree node class in HuffmanTree with necessary information is required. • You will not randomly switch left and right children when merger two trees. Instead, you will build a right-heavy tree according to the following strategies to select the right child. (1) The tree that is taller will be the right child, i.e., the height is...
We have the symbols A, B, C, D, E, F, G, H with frequencies 1, 1,...
We have the symbols A, B, C, D, E, F, G, H with frequencies 1, 1, 2, 4, 8, 16, 32, 64. Show the Huffman tree and Huffman code for the symbols. How much compression does a 1000 digit file use when using this Huffman code based on an 8-bit ASCII code (ie, ISO 8859-1)?
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more...
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more frequently can be encoded into strings of shorter lengths, while rarer letters can be turned into longer binary strings. On average, Huffman code is a more efficient way to encode a message as the number of bits in the output string will be shorter than if a fixed-length code was used....
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
3. Apply the Huffman algorithm according to the frequency chart shown below. (10 points) a. Show your work for combining the characters and frequencies. b. Assemble and show the finished tree. c. State the encoding for each character. d. Show your calculation and state the compression ratio. e. Using your Huffman tree from this question, encode the string ABACABAD. f. Using your Huffman tree from this question, decode the bit-string 100010111001010. symbol A B C D frequency 0.4 0.1 0.2...
9. (4) Select the best choice as Huffman code for the following symbols and their probabilities: A-0.10 C-0.17 E-0.21 B-0.21 D-0.06 F-0.25 (a) A: O, B: 10, C: 110, D: 1110, E: 11110, F: 11111 (b) A: 0,B: 10, C: 11111, D: 1110, E: 11110, F: 110 (c) A: 11110, B: 10, C: 1110, D: 11111, E: 110, F: 0 (d) A: 11111, B: 11110, C: 1110, D: 110, E: 10, F: 0 (e) A: 0,B: 01, C: 0001, D:...
Design the optimal (Huffman) code for the alphabet {a, b, c,
d, e, f, g, h, i, j, k, l}, where frequencies are given in the
table below:
Draw the appropriate decoding tree.
a 0.25 g 0.02 b 0.01 h 0.12 c 0.09 i 0.15 d 0.02 j 0.04 e 0.24 k 0.01 f 0.04 l 0.01
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more frequently can be encoded into strings of shorter lengths, while rarer letters can be turned into longer binary strings. On average, Huffman code is a more efficient way to encode a message as the number of bits in the output string will be shorter than if a fixed-length code was used....
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